lmomgpaRC {lmomco} | R Documentation

## B-type L-moments of the Generalized Pareto Distribution with Right-Tail Censoring

### Description

This function computes the “B”-type L-moments of the Generalized Pareto distribution given the parameters (xi, α, and kappa) from `pargpaRC` and the right-tail censoring fraction zeta. The B-type L-moments in terms of the parameters are

λ^B_1 = xi + α m_1 mbox{,}

λ^B_2 = α (m_1 - m_2) mbox{,}

λ^B_3 = α (m_1 - 3m_2 + 2m_3)mbox{,}

λ^B_4 = α (m_1 - 6m_2 + 10m_3 - 5m_4)mbox{, and}

λ^B_5 = α (m_1 - 10m_2 + 30m_3 - 35m_4 + 14m_5)mbox{,}

noindent where m_r = lbrace 1-(1-zeta)^{r+kappa}rbrace/(r+kappa) and zeta is the right-tail censor fraction or the probability mathrm{Pr}lbrace rbrace that x is less than the quantile at zeta nonexceedance probability: (mathrm{Pr}lbrace x < X(zeta) rbrace). Finally, the `RC` in the function name is to denote `R`ight-tail `C`ensoring.

### Usage

    lmomgpaRC(para)

### Arguments

`para` | The parameters of the distribution. Note that if the zeta part of the parameters (see `pargpaRC`) is not present then `zeta=1` is assumed.

### Value

An R `list` is returned.

`lambdas` | Vector of the L-moments. First element is λ_1, second element is λ_2, and so on.
`ratios` | Vector of the L-moment ratios. Second element is tau, third element is tau_3 and so on.
`source` | An attribute identifying the computational source of the L-moments: “lmomgpa2”.
`message` | For clarity, this function adds the unusual message to an L-moment object that the `lambdas` and `ratios` are B-type L-moments.
`zeta` | The censoring fraction. Assumed equal to unity if not present in the `gpa` parameter object.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1995, The use of L-moments in the analysis of censored data, in Recent Advances in Life-Testing and Reliability, edited by N. Balakrishnan, chapter 29, CRC Press, Boca Raton, Fla., pp. 546–560.

### See Also

`pargpa`, `pargpaRC`, `lmomgpa`, `quagpa`, `cdfgpa`

### Examples

    para <- vec2par(c(1500,160,.3),type="gpa") # build a GPA parameter set
    lmorph(lmomgpa(para))
    lmomgpaRC(para) # zeta = 1 is internally assumed if not available
    # The previous two commands should output the same parameter values from
    # independent code bases.

    # Now assume that we have the sample parameters, but the zeta is nonunity.
    para$zeta = .8
    lmomgpaRC(para) # The B-type L-moments.

[Package lmomco version 0.92 Index]